An auction is a process by which a person or persons sell an item to buyers by the process of bidding. There are several different ways that items can be auctioned off.
Types of Auctions
An English auction is one of the most common auctions, particularly popularized by the auction website eBay. In this type of an auction, the seller offers an item up for bidding. The seller will describe the attributes of the item being auctioned before bids begin. The opening bid is almost always less than what the value of the item is (for example, many auctions on eBay start out at $0.99, despite being worth upwards of thousands of dollars). Buyers can then bid up incrementally on the item. Once there are no more bids to be placed, the item goes to the highest bidder.
A dutch auction is similar to an English auction, but in this case, bidding starts at a very high price. The auctioneer lowers the price of the item, until someone is willing to purchase it. The term was popularized by auctions held by the Dutch for their tulips, which led to tulip mania, and eventually, the near-collapse of the Dutch economy.
Sealed bid first-price auction
In this auction, all potential buyers anonymously submit the most that they are willing to pay for an item. The auctioneer collects all of the bids, and the buyer who submitted the highest bid wins the item.
Sealed bid, second-price auction
This is run exactly like a sealed bid, first price auction, except that the winner of the auction gets the item for the second highest price (i.e., if the winner bids $100, and the second highest bid was $75, then the $100 bidder gets the item for $75).
Common value auction
In this auction, the seller gives no information to the sellers regarding the item for sale. However, the sellers are able to do their own research on the item prior to bidding. This type of auction is commonly used by the United States government in selling deep-sea oil drilling rights to private companies. The government only provides the location of the area of the ocean or land tract up for sale. The companies are allowed to perform their own inquiries into whether or not there may be oil in the tract up for sale, and there is no guarantee that they will find oil if they win that tract.
Penny auctions are primarily found on the internet. In this type of auction, a high-value item starts off with an asking price of $0.01. Bidders can only bid up by a penny. However, bidders have to purchase bids from the auction house, the value of which runs anywhere from $0.60 to $1.00. Every time a bid is placed on an item, the time left in the auction is reset. This continues until no bids are placed before time runs out. This is often considered a form of gambling, as the auction is extremely biased towards the house (i.e., if a computer sells for $95.00, the firm can make up to $9,499, depending on how much the bids cost the bidders). If a bidder does not win an item, they are still out all the money they spent on purchasing bids.
For a bidder, the strategy is to always bid less than what you believe the item to be, assuming that your valuation is higher than the other bidders. A bidder's value of an item may be lower or higher than the actual retail value of the item for auction, and it differs amongst potential bidders (for example, hard-to-find popular retail items are usually sold for higher than the actual retail price on eBay).
In the case of a second-price auction, it is advantageous to bid your true value, assuming that it is higher than all the other bidders valuations.
Auctions & Game Theory
An example using game theory is listed below. In this case, if both players bid the same amount, then the payout in parentheses is assumed to be half of the value, as they are equally likely to win the auction (usually through some means of a tie-breaker). The values in parantheses are (Bidder #1 bid - Bidder #1 true value, Bidder #2 bid - Bidder #2 true value). If one player bids higher than the other, the other bidder gets 0 (they don't get the item and don't spend any money). The Nash equilibriums are marked with an asterisk:
|Bidder #2 bids $3 (overbid)||Bidder #2 bids $2 (their true value)||Bidder #2 bids $1 (underbid)|
|Bidder #1 bids $3 (overbid)||(-1, -0.5)||(-2, 0)||(-2, 0)|
|Bidder #1 bids $2 (overbid)||(0, -1)||(-.05, .05)||(0, -1)|
|Bidder #1 bids $1 (their true value)||(0, -2)||(0, 1)*||(0, .05)*|
In this case, Bidder #1 has a dominant strategy of bidding $1. Therefore, if Bidder #2 bids $2, they will win the auction. For this case, if you know what another person values an item at, shave your bid to their value, and do not go over yours. 
- Penny auctions promise savings, overlook downsides USA Today, 02/06/2011
- Gardner, Roy. Games for Business and Economics; John Wiley & Sons, Inc.; Hoboken, New Jersey. (2003)